Given $ m \angle MON = 6x - 62$, and $ m \angle LOM = 3x + 71$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Solution: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 71} + {6x - 62} = {180}$ Combine like terms: $ 9x + 9 = 180$ Subtract $9$ from both sides: $ 9x = 171$ Divide both sides by $9$ to find $x$ $ x = 19$ Substitute $19$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 3({19}) + 71$ Simplify: $ {m\angle LOM = 57 + 71}$ So ${m\angle LOM = 128}$.